September 26, 2001 University of Rochester 1
The Mirror Crack’d*: History and Status of CP Violation Studies
Eric Prebys (UR ‘90*), Fermi National Accelerator LaboratoryRepresenting the
BELLE Collaboration
*apologies to Agatha Christie
September 26, 2001 University of Rochester 2
The BELLE Collaboration
Academia Sinica Aomori University
Budker Inst. of Nuclear Physics Chiba University
Chuo University University of Cincinatti
Fukui University GyeongSang National University
University of Hawaii Institute of High Energy Physics
Institute of Single Crystal Joint Crystal Collab. Group
Kanagawa University KEK
Korea University Krakow Inst. of Nuclear Physics
Kyoto University Melbourne University
Mindanao State University Nagasaki Inst. of App. Science
Nagoya University Nara Women's University
National Lien Ho Colledge of T&C National Taiwan University
Nihon Dental College Niigata University
Osaka University Osaka City University
Princeton University Saga University
Sankyun Kwan University Univ. of Science & Technology of China
Seoul National University Sugiyama Jyogakuin University
University of Sydeny Toho University
Tohoku University Tohoku-Gakuin University
University of Tokyo Tokyo Metropolitan University
Tokyo Institute of Technology Tokyo Univ. of Agricult. & Tech.
Toyama N.C. of Martime technology
University of Tsukuba
Utkal University Virginia Polytechnic Institute
Yonsei University
300 people from 49 Institutions in 11 Countries:
Australia, China, India, Korea, Japan, Philippines, Poland, Russia, Taiwan,
Ukraine, and USA
September 26, 2001 University of Rochester 3
Just to set the tone….
Dear Eric,
I just returned to Rochester and I am happy to know that Tom has invited you for a colloquium on Sep 26. Can you send me a title of your talk at the earliest. I would like to tell you a few things that Tom may not have mentioned. First, you will be the first speaker of the semester and, therefore, you carry a great responsibility for presenting a very good
colloquium. Second, since our colloquium attendance has thinned over the years (because of bad talks, specialized talks), I have assured the students that I will only invite extraordinary speakers who can give a very general talk to graduate students across all disciplines. So, I would like you to prepare your talk keeping this in mind. In particular, what
this means is that please do not make it a talk on experimental physics, rather on physics. Remember the time when you were a student and the kinds of things you hated in colloquia, please avoid them . Not all the students will be from high energy physics. In fact, many are from optics, astronomy and so a talk with less display of detectors etc and with a greater balance of theoretical motivation and the explanation of results would be highly appreciated.
Why am I telling you all this? Well, first of all, you were our former student and as such I have a right to ask you for things. Second, you will be the first speaker and if the students are not thrilled with your talk, the attendance may shrink in the subsequent talks. On the other hand, if your talk is superb, which I hope it will be, more people will show up for the later talks (people have a tendency to extrapolate). In any case, please keep in mind that you will be talking to a general audience and not to a group of experimentalists.
Let me know when your itinerary is complete, but please send me a title in a couple of days.
With very best regards,
Ashok.
September 26, 2001 University of Rochester 4
Outline
• Why do we care?
• History – Parity Violation
– V-A Currents and CP (almost) Conservation
– CP Violation in the Neutral K System
– The Cabbibo-Kobayashi-Maskowa Mechanism
– “The” Unitarity Triangle
• The Present– Direct CP Violation in the Neutral K System (’/)
– Indirect CP Violation in the B meson System (B-Factories)
• The Future?
September 26, 2001 University of Rochester 5
Why do We Care?
• Dirac first predicted antimatter in 1930 as a consequence of the “extra” solutions to his relativistic formulation of quantum mechanics - and was widely ridiculed.
• The positron (anti-electron) was discovered by Anderson in 1932 and the anti-proton was discovered by Segre and Chamberlain in 1955.
• Now we are all quite comfortable with the idea of antimatter as “equal and opposite” to matter, e.g.
• …but why does the universe seem to be made entirely of matter?
• Why do there seem to be tiny differences in the physics of matter and antimatter?
• These legitimately qualify as “big questions”.
“Of course, there is only one correct mixing ratio of matter and
antimatter: one to one!” – Star Trek, The Next Generation
September 26, 2001 University of Rochester 6
Parity Violation
• The “parity” operation transforms the universe into its mirror image (goes from right-handed to left-handed).
• Maxwell’s equations are totally parity invariant.
• BUT, in the 50’s huge parity violation was observed in weak decays…
5J
Co60
4J
Ni*60
e
e
Example decay of polarized Co... electron preferentially emitted opposite spin direction
x
y
z
x
y
z
September 26, 2001 University of Rochester 7
Weak Currents and Parity Violation
BDACDBCA uuuujjA
,
AAvC uccuj 5
Ae
*Be
Ce
De
Review: QEDEMj
,EMjTransform like vectors
For weak interactions, try (“four fermion interaction”)
Ae
B
C
De
,weakj
weakj
vector
axial vector
Manifestly Violates Parity!!
September 26, 2001 University of Rochester 8
“V-A” Current
ACweak uuj 5
Experimentally, it was found that data were best described by
Maximum Parity Violation!!!!
Recall that for Direct Spinors, the left handed projection operator is
LLweakLL uujuuPu
2
1 5
“Left-handed” current
For massless particles, spinor state = helicity state
Only Left-handed Neutrinos
September 26, 2001 University of Rochester 9
CP Conservation (sort of)
When we apply the usual Dirac gymnastics, we find that for anti-particles
RRACweak vvvvj 5Right-handed current
Only Right-handed anti-Neutrinos
Overall symmetry restored under the combined operations of C(harge conjugation) and P(arity).
CP Conservation!!!
well, maybe not….
September 26, 2001 University of Rochester 10
The Neutral Kaon System
In experiments in the 1950s, it was found that there were two types of neutral strange particles, of indistinguishable mass (498 MeV), but with different decay properties.
2
3
)(
)(
hortS
ongL
K
K CP = -1
CP = +1 Because 3*m mK , the KL lives about 600 times longer than the KS, hence the
names.
Possible explanation: 00
00
2
12
1
KKK
KKK
L
S
Strangeness eigenstates
close, but not quite correct…
September 26, 2001 University of Rochester 11
CP Violation in the Neutral K System
In 1964, Fitch, Cronin, etal, showed that in fact KL2 with a branching ratio on the order of 10-3.
Interpretation:
002
001
2
12
1
KKK
KKK
3
12
21
103.2
KKK
KKK
L
S
CP Eigenstates
Mass Eigenstates
SK
LK
s)10( 105 10 15
September 26, 2001 University of Rochester 12
The Significance
In other words…
0,
0,, KbKaK SLSLSL where SLSL ba ,,
This generated great interest (not to mention a Nobel Prize), and has been studied in great detail ever since, but until recently had only been conclusively observed in the kaon system.
Unlike parity violation, it is not trivial to incorporate CP violation into the standard model. To understand how it is done, we must now digress a bit into some details of fundamental particle interactions….
September 26, 2001 University of Rochester 13
Weak Interactions in the Standard Model
• In the Standard Model, the fundamental particles are leptons and quarks
• In this model, weak interactions are analogous to QED.
e
e e
W
e u
W
d
OR
qqqqqqqq or , ,
quarks combine as
to form hadrons
leptons exist
independently
September 26, 2001 University of Rochester 14
Quark Mixing
b
t
s
c
d
u
ee
In the Standard Model, leptons can only transition within a generation (NOTE: probably not true!)
Although the rate is suppressed, quarks can transition between generations.
September 26, 2001 University of Rochester 15
The CKM Matrix (1973)
• The weak quark eigenstates are related to the strong (or mass) eigenstates through a unitary transformation.
b
s
d
VVV
VVV
VVV
b
s
d
tbtstd
cbcscd
ubusud
'
'
'
''' b
t
s
c
d
u
Cabibbo-Kobayashi-Maskawa (CKM) Matrix
• The only straightforward way to accommodate CP violation in the SM is by means of an irreducible phase in this matrix
• This requires at least three generations and led to prediction of t and b quarks … a year before the discovery of the c quark!
d
W
uudVd
W
u*
udV
September 26, 2001 University of Rochester 16
Wolfenstein Parameterization
1)1(
21
)(21
23
22
32
AiA
A
iA
The CKM matrix is an SU(3) transformation, which has four free parameters. Because of the scale of the elements, this is often represented with the “Wolfenstein Parameterization”
CP Violating phaseFirst two generations almost
unitary. = sine of “Cabbibo Angle”
September 26, 2001 University of Rochester 17
“The” Unitarity Triangle
• Unitarity imposes several constraints on the matrix, but one (product first and third columns)...
0*** ubudcbcdtbtd VVVVVVresults in a triangle in the complex plane with sides of similar length , and appears the most interesting for study 3A
*tbtdVV*
ubudVV
*cbcdVV
13
2
) , , : USin (Note! 321
September 26, 2001 University of Rochester 18
The Plane
• Remembering the Wolfenstein Parameterization
1)1(
21
)(21
23
22
32
AiA
A
iA
we can divide through by the magnitude of the base (A3)….
*
*
cbcd
ubud
VV
VV
13
2*
*
cbcd
tbtd
VV
VV
0,0 0,1
ηρ,
CP violation is generally discussed in terms of this plane
September 26, 2001 University of Rochester 19
Direct CP Violation
• CP Violation is manifests itself as a difference between the physics of matter and anti-matter
)()( fifi • Direct CP Violation is the observation of a difference between
two such decay rates; however, the amplitude for one process can in general be written
swsw iiii AAAA eeee
Weak phase changes sign Strong phase does not
• Since the observed rate is only proportional to the amplitude, a difference would only be observed if there were an interference between two diagrams with different weak and strong phase.
Rare and hard to interpret
September 26, 2001 University of Rochester 20
Direct CP Violation in the Neutral Kaon System (’/ Measurement)
12
21
KKK
KKK
L
S
Recall…
If there is only indirect CP violation, then ALL 2 decays really come from K1 , and we expect (among other things)
)(
)(
)(
)(
)(
)(0000
1
100
S
S
L
L
KBr
KBr
KBr
KBr
KBr
KBr
But the Standard Model allows
2
)2()2(
2
00
K
KBrKBr
Direct CP Violation
September 26, 2001 University of Rochester 21
Direct CP Violation in the Neutral Kaon System (cont’d)
12 KKKL
’
CP=+1CP=-1
CP=+1
Formalism:
'2)(
)(
')(
)(
00
00
00
S
L
S
L
KA
KA
KA
KA
)/'Re(61)(/)(
)(/)(2
000000
SL
SL
KBrKBr
KBrKBr
Theoretical estimates for ’range from 4-30 x 10-4
September 26, 2001 University of Rochester 22
Easy to Measure….NOT!
00LK
00
SK
DetectorMust take great steps to understand acceptances and systematic errors!!
September 26, 2001 University of Rochester 23
KTeV Experiment (Fermilab)
(Images from Jim Graham’s Fermilab “Wine and Cheese” Talk)
September 26, 2001 University of Rochester 24
Current Status of ’
At this point, the accuracy of this measurement is better than that of the theoretical prediction:
(4-30 x 10-4)
(ibid.)
This bothered people
September 26, 2001 University of Rochester 25
Indirect CP Violation in the B Meson System
• Let’s Look at B-mixing…
022
02
(0 sincos)( BeiBetB mimtmtimi
d t b
t db
V td V tb
*
V tb
*
V td
0B 0BW W
Mixing phase 1* )arg( tbtdVV
September 26, 2001 University of Rochester 26
Indirect CP Violation (cont’d)
• If both can decay to the same CP eigenstate f, there will be an interference
BB and
0B0B
f
And the time-dependent decay probability will be
Decay phase
CP state of f Mixing phase
)*sin()sin(1eP(t) || tmDMCPt
Difference between B mass eigenstates
September 26, 2001 University of Rochester 27
The Resonances
e
e
b
b
*
b
b
b
b
b
b
u
u
B
B
b
b
b
b
d
d
0B
0B
At the right energies, electrons and positrons can produce a spectrum of bound resonant states of b and anti-b quarks
The 1- states are called the “ (‘Upsilon’)resonances”
Starting with the (4S), they can decay strongly to pairs of B-mesons.
The lighter states must decay through quark-antiquark annihilation
September 26, 2001 University of Rochester 28
The Basic Idea
• We can create pairs at the resonance.
• Even though both B’s are mixing, if we tag the decay of one of them, the other must be the CP conjugate at that time. We therefore measure the time dependent decay of one B relative to the time that the first one was tagged (EPR “paradox”).
• PROBLEM: At the resonance, B’s only go about 30 m in the center of mass, making it difficult to measure time-dependent mixing.
S)4(
S)4(
00 BB
e-e
0B
0Bm 30
September 26, 2001 University of Rochester 29
The Clever Trick (courtesy P. Oddone)
• If the collider is asymmetric, then the entire system is Lorentz boosted.
• In the Belle Experiment, 8 GeV e-’s are collided with 3.5 GeV e+’s so
e-e
0B
0Bm 30
e-e
0B
0Bm 200
• So now the time measurement becomes a z position measurement.
September 26, 2001 University of Rochester 30
“Gold-Plated” Decay
d
b
0Bc
s
c
d
W
)1(),1( CPKCPK LS
/JV cb
*
V cs
0)arg( * cbcsD VV
)( probes 1 M
etc) ,,( ee
00,
Total state CP
September 26, 2001 University of Rochester 31
Predicted Signature
t = Time of tagged decays
September 26, 2001 University of Rochester 32
“Tin-Plated” Decay
d
b0B
d
u
u
d
W
V ub
*
V ud
)()arg( 21* ubudD VV
)( )( probes 2121 DM
Complicated by “penguin pollution”, but still promising
September 26, 2001 University of Rochester 33
• Make LOTS of pairs at the (4S) resonance in an asymmetric collider.
• Detect the decay of one B to a CP eigenstate.
• Tag the flavor of the other B.
• Reconstruct the position of the two vertices.
• Measure the z separation between them and calculate proper time separation as
• Fit to the functional form
• Write papers.
• Over the last ~8 years, there have been two dedicated experiments under way to do this – BaBar (SLAC) and Belle (KEK)
Review - What B-Factories Do...
bb
)/( czt CMCM
tmCPt sin2sin1e 1||
September 26, 2001 University of Rochester 34
Motivations for Accelerator Parameters
• Must be asymmetric to take advantage of Lorentz boost.
• The decays of interest all have branching ratios on the order of 10-5 or lower.– Need lots and lots of data!
• Physics projections assume 100 fb-1 = 1yr @ 1034 cm-2s-1
• Would have been pointless if less than 1033 cm-2s-1
September 26, 2001 University of Rochester 35
The KEKB Collider (KEK)
• Asymmetric Rings– 8.0GeV(HER)
– 3.5GeV(LER)
• Ecm=10.58GeV= M((4S))
• Target Luminosity: 1034s-1cm-2
• Circumference: 3016m
• Crossing angle: 11mr
• RF Buckets: 5120 2ns crossing time
September 26, 2001 University of Rochester 36
The PEP-II Collider (SLAC)
• Asymmetric Rings– 9.0GeV(HER)
– 3.1GeV(LER)
• Ecm=10.58GeV= M((4S))
• Target Luminosity: 3x1033s-1cm-2
• Crossing angle: 0 mr
• 4ns crossing time
September 26, 2001 University of Rochester 37
Motivation for Detector Parameters
• Vertex Measurement
– Need to measure decay vertices to <100m to get proper time distribution.
• Tracking…
– Would like p/p.5-1% to help distinguish B decays from BK and BKK decays.
– Provide dE/dx for particle ID.
• EM calorimetry
– Detect ’s from slow, asymmetric ’s need efficiency down to 20 MeV.
• Hadronic Calorimetry
– Tag muons.
– Tag direction of KL’s from decay BKL .
• Particle ID
– Tag strangeness to distinguish B decays from Bbar decays (low p).
– Tag ’s to distinguish B decays from BK and BKK decays (high p).
Rely on mature, robust technologies whenever possible!!!
September 26, 2001 University of Rochester 38
The Belle Detector
September 26, 2001 University of Rochester 39
BaBar Detector (SLAC)
September 26, 2001 University of Rochester 40
The Accelerator is Key!!!
STOP Run +HV Down +Fill HER +Fill LER +HV Up +START Run
= 8 Minutes!
September 26, 2001 University of Rochester 41
Luminosity
Daily integrated luminosity
Total integrated luminosity
Total for first CP Results (Osaka): -1fb 2.6
Total for these Results:-1fb 9.12
Our Records:
•Instantaneous:
•Per (0-24h) day:
•Per (24 hr) day:
•Per week:
•To date:
-1-233 scm 1049.4 -1pb 29.12
-1fb 9.29
-1pb 4781
-1pb 41.32
(on peak)
Note: integrated numbers are accumulated!
World Records!!
September 26, 2001 University of Rochester 42
The Pieces of the Analysis
• Event reconstruction and selection
• Flavor Tagging
• Vertex reconstruction
• CP fitting
September 26, 2001 University of Rochester 43
J/ and KS Reconstruction
ee
SK
Mev
Require mass
within 4of PDG
September 26, 2001 University of Rochester 44
BKS Reconstruction
• In the CM, both energy and momentum of a real B0 are constrained.
• Use “Beam-constrained Mass”:
222 pEM beamBC
Signal
123 Events
3.7 Background
September 26, 2001 University of Rochester 45
All Fully Reconstructed Modes (i.e. all but L)
Mode Events Background
BS 457 12
All Others 290 46
Total 747 58
September 26, 2001 University of Rochester 46
BKL Reconstruction
• Measure direction (only) of KL in lab frame
• Scale momentum so that M(KL+)=M(B0)
• Transform to CM frame and look at p(B0).
KLM Cluster
J/ daughter particles
KL
September 26, 2001 University of Rochester 47
BKL Signal
0<pB*<2 GeV/c
Biases spectrum!
346 Events
223 Background
September 26, 2001 University of Rochester 48
Flavor Tagging
d
b
0B
or ,,,, eescsudu
s
c
X
q
etc. ,,,, 0 KK
W
opposites. theproduce wills' while,and/or ,,e
momentum high produce to tend wills' lly,Statistica0
0
BK
B
September 26, 2001 University of Rochester 49
Flavor Tagging (Slow Pion)
d
b
0B
or ,,,, eescsudu
c
W
*Dud
uc 0D
Very slow pion
. slow produce to tend wills'0 B
Combined effective efficiency eff = t(1-2w)2 = 27.0.2%
September 26, 2001 University of Rochester 50
Vertex Reconstruction (SVD)
Overall efficiency = ~85%. In total 1137 events for the CP fit.
September 26, 2001 University of Rochester 51
CP Fit (Probability Density Function)
1 1( ;sin 2 ) e 1 sin 2 sin
(1 ) ( ) ( ) d ( )
B
t
dB
BG BG BG
tf t x
PDF f f t R t t t f PDF t
•fBG = background fraction. Determined from a 2D fit of E vs M.
•R( t) = resolution function. Determined from D*’s and MC.
•PDFBG( t) = probability density function of background. Determined from sideband.
September 26, 2001 University of Rochester 52
Resolution Function
018.0
ps 78.3
ps 78.0
ps 54.1
ps 09.0
tail
tail
tail
main
main
f
Fit with a double-Gaussian…
September 26, 2001 University of Rochester 53
Test of Vertexing – B Lifetime
ps) 03.65.1 :(PDG ps 03.64.1
ps) 03.55.1 :(PDG ps 02.55.10
B
B
September 26, 2001 University of Rochester 54
The Combined Fit (All Charmonium States)
September 26, 2001 University of Rochester 55
Sources of Systematic Error
• Bottom Line
.)(06.)(14.99.2sin 1 syststat Published in Phys.Rev.Lett. 87, 091802 (2001)
September 26, 2001 University of Rochester 56
The BaBar Measurement
05.14.59.2sin
Phys.Rev.Lett. 87 (2001)
Based on 32 million B-Bbar pairs
September 26, 2001 University of Rochester 57
Summary of 21 Measurements
September 26, 2001 University of Rochester 58
How About That Plane?
World Average Sin21 (1)
Constraints of Everything but Sin21
Looks good for the Standard Model, but a little dull for experimenters !
September 26, 2001 University of Rochester 59
Current Status
• The study of CP Violation has been going on for almost 40 years! • A number of experiments are currently taking data which seem to
be confirming the Standard Model (CKM) explanation of CP Violation, and thereby constraining that model– Direct CP violation is observed in the neutral K system!– CP is violated in the B-Meson system!
• Over the next several years, the existing B-Factories will continue to take data, providing tighter and tighter constraints.
• New players are also coming on the scene:– Fermilab Run II (CDF and D0) - now– BTeV (dedicated B Experiment at Fermilab) - ~2005– LHC (Atlas and CMS) - 2006– LHC-B (dedicated B Experiment at LHC) - ?
September 26, 2001 University of Rochester 60
More “Out There”
• CP Violation in the sector? (probably there, hard to study)
• CPT Violation?– CPT Conservation is a direct consequence of the Lorentz invariance of the
Lagrangian.
– Evidence of its violation would be observation (direct or indirect) of
and would be big news.
• We still can’t answer why the unverse is all matter. Maybe it isn’t!– The AMS experiment, set to fly on the ISS, will look for massive anti-
nuclei to test the hypothesis that distant parts of the universe might be antimatter (!!)
)()(or )()( pppmpm
September 26, 2001 University of Rochester 61
Are Two B-Factories Too Many?
• These are not discovery machines!
• Any interesting physics would manifest itself as small deviations from SM predictions.
• People would be very skeptical about such claims without independent confirmation.
• Therefore, the answer is NO (two is not one too many, anyway).
September 26, 2001 University of Rochester 62
Differences Between PEP-II (BaBar) and KEKB (Belle)
•PEP-II has complex IR optics to force beams to collide head-on.Pros: Interaction of head-on beams well understood.Cons: Complicates IR design.
More synchrotron radiation.Can’t populate every RF bucket.
• In KEK-B, the beams cross at ±11 mr.Pros: Simple IR design.
Can populate every RF bucket.Lower (but not zero!!!) synchrotron radiation.
Cons: Crossing can potentially couple longitudinal and transverse instabilities.
At present, both designs seem to be working.
September 26, 2001 University of Rochester 63
Differences (cont’d)
Readout:
• BaBar uses an SLD-inspired system, based on a continuous digitization. The entire detector is pipelined into a software-based trigger.
Pros: Extremely versatile trigger.Less worry about hardware-based trigger systematics.Can go to very high luminosities.
Cons: Required development of lots of custom hardware.
• Belle’s readout is based on converting signals to time-pulses. The trigger is an “old-fashioned” hardware-based level one. Events satisfying level one are read out after a 2 µs latency.
Pros: Simple.Readout relies largely on “off-the-shelf” electronics.
Cons: Potential for hardware-based trigger systematics.Possible problems with high luminosity.
September 26, 2001 University of Rochester 64
Particle ID needs
Technology Pros Cons Comment
TOF Simple. Only for lowmomentum.
Included inBelle
dE/dx Proven.Comes for
free.
Only for lowmomentum
Included inBelle.
TMAE basedRICH
Proven inSLD andDELPHI
Universallydespised.
Rejected.
CSI RICH Once seemedpromising.
No one couldbuild aworking
prototype.
Rejected.
DIRC Rugged.Excellentseparation.
New.Contstrantson detectorgeometry
Babar choice
AerogelthresholdCerenkov
Simple. Barelyadequate
Belle choice